A necessary condition is established for the lossy transmission of correlated sources over a memoryless multiple- access channel (MAC). It is used to derive lower bounds on the symmetric distortions that are achievable over Gaussian and binary adder MACs. When specialized to symmetric Gaussian MACs and Gaussian sources, the new lower bound recovers Lapidoth and Tinguely’s max-correlation lower bound (2010) when the channel bandwidth is equal to the source bandwidth, and it improves on it when the channel bandwidth is higher.